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JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Question Bank Mock Test - Gravitation and Mechanical Properties of Solid

  • question_answer
    A rocket of mass \[M\] is launched vertically from the surface of the earth with an initial speed \[V\] Assuming the radius of the earth to be \[R\] and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is

    A) \[R/\left( \frac{gR}{2{{V}^{2}}}-1 \right)\]                     

    B) \[{{R}_{{}}}\left( \frac{gR}{2{{V}^{2}}}-1 \right)\]

    C) \[R/\left( \frac{gR}{2{{V}^{2}}}-1 \right)\]        

    D) \[R\left( \frac{2gR}{{{V}^{2}}}-1 \right)\]

    Correct Answer: C

    Solution :

    [c] \[\Delta K.E.=\Delta U\] \[\Rightarrow \frac{1}{2}M{{V}^{2}}=G{{M}_{e}}M\left( \frac{1}{R}-\frac{1}{R+h} \right)\]                  (i) Also \[g=\frac{G{{M}_{e}}}{{{R}^{2}}}\]                                           (ii) On solving (i) and (ii), \[h=\frac{R}{\left( \frac{2gR}{{{V}^{2}}}-1 \right)}\]


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